I think the main trick is spending a whole lot of Yen (on registered Persona) or having a whole lot of Persona that you probably don't want to waste slots, keeping. You'll get a boost if your Persona matches the S-link of the visit, thats what all the added text is about before you tackling a link.

My guess, doing that regularly, will be most economical way to cause events to happen one after another. What I don't know is if it matters, of how many matching Persona you have in your inventory, when you visit them. If it matters than more would make things go even faster.

You'll probaly need a run with almost no dud events to get all the links. This game is really a, "hind sight is 20/20", type game. If you activate 2 duds in a row, then you realize that you should have visited the Shrine that first time. The problem is that a game week has usually passed, before you realize that, and you've probably spent hours in Taturus...

General guideline would be:

The Hermit is a Shrine visit, must; I can guarantee that much. That one sucks up a whole day and warns you, if the wasted day is going to be worth it.... or not via the text about a blinking light. So, if it's not blinking on a Sunday or vacation day, your best option is to waste a period at the shrine's relationship thing.

Sun, will have you cancelling phone dates, quite regularly, and the game events will rob you of your Sundays quite often, as well, making this link taking well over 2 months to achieve. This is the link that you'll want to continue after completeing the Hermit one.... or vice versa. Vice versa would be the better way to go, because it'll give you extra late night studying time, where as the Hermit takes up the whole day. (Although, there is at least one day that falls on a Sunday, where you can get a Hermit day in, and not lose the whole day... that I can recall. Maybe more than one...)

Saturdays are the best day to do date links, or outside links... School date links is probably the best use, because the vacations will keep you from doing them otherwise.

Outside links are best to tackle when school isn't available... Although, you'll have to start at least one while school is in session, to get an item to activate it. And then it'll also activate a new S-links within the school period. But you should be able to get through all that with no real penelty, in the early phases of the game, being that the in-school ones are generally unlocked via the calendar and you'll have very little to do other than continue that outside S-link

Classrooms and Student councel are all fixed on certain days, so you'll just have to juggle those, within the school year.

Also, probably best to do the "date ones", one at a time, once one goes past level 4 for all of them. Suggest activating all of them to at least number 1, before a little after coming back from school vacation, so to witness a comical scene. (which you've already past).

The night ones are a given... just need to cancel the dungeon trip for those and you can study late as a bonus, and if you get sick/tired you can then go to the nurse for another bonus.

Honestly, I seriously doubt it's possible to do them all in one go without losing some, if not all, of the game's fun in the process. There are a lot of added events that do very little other than enhance one of your 3 stats, but are fun to watch. And most often than not, you'll have the stats already maxed, by the time the game starts activating them. Where as, if you are solely doing S-links the better option would be not to attend such special events... and miss whatever dialog/scene it has, there.